Synaptic connectivity between neurons is naturally constrained by the anatomical overlap of neuronal arbors, the space on the axon available for synapses, and by physiological mechanisms that form synapses at a subset of potential synapse locations. What is not known is how these constraints impact emergent connectivity in a circuit with diverse morphologies. We investigated the role of morphological diversity within and across neuronal types on emergent connectivity in a model of neocortical microcircuitry. We found that the average overlap between the dendritic and axonal arbors of different types of neurons determines neuron-type specific patterns of distance-dependent connectivity, severely constraining the space of possible connectomes. However, higher order connectivity motifs depend on the diverse branching patterns of individual arbors of neurons belonging to the same type. Morphological diversity across neuronal types, therefore, imposes a specific structure on first order connectivity, and morphological diversity within neuronal types imposes a higher order structure of connectivity. We estimate that the morphological constraints resulting from diversity within and across neuron types together lead to a 10-fold reduction of the entropy of possible connectivity configurations, revealing an upper bound on the space explored by structural plasticity.